The slope of the tangent to the curve $y = \int_0^x \frac{1}{1+t^3} dt$ at the point where $x = 1$ is

The length of the subtangent to the curve $x^2 y^2 = a^4$ at the point $(-a, a)$ is

For the curve $4x^{5} = 5y^{4}$,the ratio of the cube of the subtangent at a point on the curve to the square of the subnormal at the same point is

If the length of the subnormal is equal to the length of the subtangent at any point on the curve $y = f(x)$ and the tangent at $(3, 4)$ to $y = f(x)$ meets the positive coordinate axes at $A$ and $B$,then the area of $\Delta OAB$,where $O$ is the origin,is

What are the lengths of the intercepts on the coordinate axes made by the tangent to the curve $y = 2x^2 + 3x - 2$ at the point $(1, 3)$?

The point at which the tangent to the curve $y = 2x^2 - x + 1$ is parallel to $y = 3x + 9$ will be